Inspired by previous work of Bruinier-Ono and Mertens-Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the irreducibility of class polynomials and obtain a general theorem to check when functions constructed in a special way are class invariants.
We define the doubling zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that there exists an apropriate normalizing factor which allows us to construct γ-factors for smooth families out of the functional equation. We prove that under certain hypothesis, specializing this γ-factor at a point of the family yields the γ-factor defined by Piateski-Shapiro and Rallis.
We define the doubling zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that there exists an appropriate normalizing factor that allows us to construct $\gamma $-factors for smooth families out of the functional equation. We prove that under certain hypothesis, specializing this $\gamma $-factor at a point of the family yields the $\gamma $-factor defined by Piateski–Shapiro and Rallis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.